SUPPLEMENT 2 - ON LINE – CALCULATION OF THE KNEE AND HIP MOMENTS 1
FROM THE iRPF 2
The instrumented Running Prosthetic Foot22 was developed for measuring the loads acting on the 3
foot in a Foot Reference Frame during in-vivo field or laboratory testing.
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Its sensing principle is based on the application of three strain gauge bending bridges at three known 5
locations of the proximal end of the prosthetic foot, close to the clamp. The three bridges are presented 6
in Figure S1.1.
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Figure S1.1. Bridges of the iRPF. (a) Location of the three strain bridges. (b) Foot Reference Frame 9
and loads measured by the iRPF.
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A calibration procedure allowed to evaluate the response of the three bending strain gauge bridges to 12
known bending moments and to calculate the linear constant response of each bridge. The signal 13
output of the three bending bridges (in mV/V) can in turn be combined with the geometrical position 14
of the bridges to give the loads acting at the Foot Reference Frame Origin, named O and located on 15
BRG1, as shown in Figure S1.1.
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The knowledge of loads at Oand of the foot absolute orientation angle with respect to the horizontal 17
allows the instantaneous calculation of Ground Reaction forces GRFx and GRFy in the Global 18
Reference Frame.
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During stance, the knee is locked and the relative location of foot clamp, knee and hip does not 20
change. Therefore, if the relative distance and orientation of O, the knee center KP, and the Hip joint 21
center H (assumed as GTP) are known, it is possible to estimate the loads acting on K and H, and the 22
moment of the Ground Reaction Forces.
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The Hip reaction forces HRF, calculated as the GRF resolved in the hip reference frame, are:
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FxH= Force component at the hip, perpendicular to the socket axis, in the sagittal plane;
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FyH= Force component at the hip parallel to the socket axis, in the sagittal plane;
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MzH= Moment acting at the hip in the sagittal plane, along a lateral Z axis, positive counter- 27
clockwise in a right side view (in general, positive if flexing the hip).
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These loads can be calculated using the following formulas that adopt the geometric quantities 29
presented in Figure S1.2.
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{
𝐹𝑥𝐻 = 𝐹𝑥𝐹 ∗ sin(𝛿 − 𝛾) + 𝐹𝑦𝐹∗ 𝑐𝑜𝑠(𝛿 − 𝛾) 𝐹𝑦𝐻 = −𝐹𝑥𝐹∗ cos(𝛿 − 𝛾) + 𝐹𝑦𝐹∗ 𝑠𝑖𝑛(𝛿 − 𝛾)
𝑀𝑧𝐻= 𝑀𝑧𝐹 + 𝐹𝑥𝐹∗ 𝐺𝑇̅̅̅̅̅̅̅ ∗ 𝑠𝑖𝑛(𝛿) − 𝐹𝑦𝑃𝑄 𝐹∗ (𝑂𝑄̅̅̅̅ − 𝐺𝑇̅̅̅̅̅̅̅ ∗ 𝑐𝑜𝑠(𝛿))𝑃𝑄 32
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Where Q is the intersection point of line GTPKP with the xF axis, is the angle between GTPKP-Q 34
and the xF axis, is the angle between the GTPKP line and the socket axis.
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Figure S1.2. Sketch of the geometric quantities relating the foot to the knee and the hip.
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The Knee Moment, can be defined as:
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• MzK= Moment acting at the knee along the lateral Z axis, positive counter-clockwise (in 42
extension).
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It can be calculated as the moment applied by the Ground Reaction Forces to KP as expressed using 44
the following formulas referring to Figure S1.3:
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𝑀𝑧𝐾 = 𝑀𝑧𝐹+ 𝐹𝑥𝐹(𝐾̅̅̅̅̅̅ ∗ sin(𝛿)) − 𝐹𝑦𝑃𝑄 𝐹(𝑂𝑄̅̅̅̅ − 𝐾̅̅̅̅̅̅ ∗ cos(𝛿)) 𝑃𝑄 46
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Figure S1.3. Sketch of the geometric quantities relating the foot to the knee.
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